1. Field of the Invention
This invention relates generally to flow detection. Specifically, this invention relates to the detection of critical flow conditions in a nozzle.
2. Background Information
Nozzles are frequently used to measure the flow rate of gas through a pipeline. When a nozzle is inserted in a flowing stream of gas, the flow rate through the nozzle will increase or decrease in proportion to the ratio of the downstream pressure (P.sub.2) to the upstream pressure (P.sub.1) in the flow line up to the point at which the average gas velocity reaches the speed of sound in the throat of the nozzle. The ratio of the downstream pressure to upstream pressure at this point is called the critical pressure ratio (r.sub.c). Below this ratio, the gas flow rate through the nozzle is not affected by P.sub.2, but instead, is a function of P.sub.1 only (assuming all other conditions remain constant). Nozzles operated below the r.sub.c are commonly referred to as "critical flow nozzles" and are especially useful in flow measurement because of their dependence only on P.sub.1. An application of the utility of critical flow nozzles is found in copending application Ser. No. 874,731 filed June 16, 1986, assigned to the assignee of the present invention, and is incorporated by reference herein for all purposes.
A common problem in the use of critical flow nozzles is in determining the point at which critical flow is obtained. Perry et al ("Chemical Engineers Handbook," Fifth Edition, pages 5-11 to 5-12, incorporated by reference herein) describes various equations which can be used in estimating the critical pressure ratio. For an ideal gas, the critical pressure ratio can be described by the equation: ##EQU1## and for .beta.&lt;0.2 can be approximated by: ##EQU2##
The above equations are useful in providing an initial estimate of the critical pressure ratio. However, these equations assume, among other things, that the gas behaves as an ideal gas, and that the ratio of specific heats is precisely known. This is frequently not the case, especially in oil field operations where gas lines may be operated at extremely high pressure and where the gas stream may be a complex mixture of gases, many of which are known to exhibit non-ideal behavior at relatively low pressure (e.g. CO.sub.2). Therefore, if an accurate determination of gas flow rate is desired, the nozzle will frequently be operated at pressure ratios much lower than calculated in the above equation to provide a margin of safety. This results in unnecessary pressure drop in the pipeline which can translate into significant compression costs. Further, in some cases, excess compression capacity may not be available to provide this pressure.
In summary, it is desirable to devise a method of accurately determining the point at which a nozzle has reached critical flow conditions.